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%I #44 Dec 22 2023 12:10:58
%S 0,0,0,0,1,0,1,0,1,0,2,0,2,0,2,0,3,0,3,0,3,0,4,0,4,0,4,0,5,0,5,0,5,0,
%T 6,0,6,0,6,0,7,0,7,0,7,0,8,0,8,0,8,0,9,0,9,0,9,0,10,0,10,0,10,0,11,0,
%U 11,0,11,0,12,0,12,0,12,0,13,0,13,0,13,0,14,0,14,0,14
%N a(n) = a(n-2) + a(n-6) - a(n-8) with n>8, the first eight terms are 0 except that for a(5) = a(7) = 1.
%C Sequence related to A264041 (1 is the offset of A264041).
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,0,0,1,0,-1).
%F G.f.: x^5/(1-x^2-x^6+x^8).
%F a(n) = A264041(n) - n*(n+1)/2, 0<n<=26 (conjectured for n>26).
%F a(n) = (1-(-1)^n)*floor(n/6+1/3)/2. [_Bruno Berselli_, Nov 10 2015]
%p with(numtheory): P:= proc(q) local n; for n from 0 to q do
%p print((1-(-1)^n)*floor(n/6+1/3)/2); od; end: P(100); # _Paolo P. Lava_, Nov 12 2015
%t LinearRecurrence[{0, 1, 0, 0, 0, 1, 0, -1}, {0, 0, 0, 0, 1, 0, 1, 0}, 100]
%t Table[(1 - (-1)^n) (Floor[n/6 + 1/3]/2), {n, 1, 90}] (* _Bruno Berselli_, Nov 10 2015 *)
%o (PARI) concat(vector(4), Vec(x^5/(1-x^2-x^6+x^8) + O(x^100))) \\ _Altug Alkan_, Nov 10 2015
%o (Sage) [(1-(-1)^n)*floor(n/6+1/3)/2 for n in (1..90)] # _Bruno Berselli_, Nov 10 2015
%Y Cf. A000004 (second bisection), A000217, A002264 (for the first bisection), A264041.
%K nonn,easy
%O 1,11
%A _Jean-François Alcover_ and _Paul Curtz_, Nov 09 2015
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